So I bought this for my mother who lives very far away, and is somewhat difficult to work with over the phone. I ordered the Chromebook from gilt.com and had it very early, before June 30. She's been fine with it this whole time.
So suddenly she gets "your password has changed" and throwing a captcha apparently after entering her password on the main login screen or possibly by simply clicking her name. She tried using the [+] symbol to create a new user and tried her username and her username @gmail.com and neither work.
I changed her password on my end via Google Accounts and had her shut down and start up and try the new password. At this point, it stopped showing the "your password has changed" but continues throwing a captcha which when entered correctly several times, doesn't work.
I changed her password to something simple and she tried the captcha many times, with no luck. It's just refusing to let her in.
This guy seems to have had the same problem and implied a factory reset may be needed:
InformationWeek Mobile Edition - News >> - Samsung Series 5 Chromebook: Hands-On Review
Ok new development...
After more attempts, she got "Your google account password had changed since the last time you signed in. Synchronize all settings and data, only synchronize data and settings that have changed since last sign in" with synchronize all settings and data by default.
She chose the first one, and at this point it went black, and started throwing things like "Erasing stateful partition..." until it eventually came to "Let's get started...". So now my mom has to go through the whole setup as if she just took it out of the box. /sigh well at least hopefully we won't have to go through a hard reset.